mlsanityData to 7 Oct 2026

Reachability Analysis of Deep Neural Networks with Provable Guarantees

arXiv 1805.02242 ↗First posted 6 May 2018cs.LG cs.CV stat.MLcited by 93

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Abstract (arXiv)

Verifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs, computes the lower and upper bound on the function values. Because the network and the function are Lipschitz continuous, all values in the interval between the lower and upper bound are reachable. We show how to obtain the safety verification problem, the output range analysis problem and a robustness measure by instantiating the reachability problem. We present a novel algorithm based on adaptive nested optimisation to solve the reachability problem. The technique has been implemented and evaluated on a range of DNNs, demonstrating its efficiency, scalability and ability to handle a broader class of networks than state-of-the-art verification approaches.

Key facts. Cited by 93 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 May 2018.

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Citing papers per year: 2021: 29; 2022: 19; 2023: 19; 2024: 17; 2025: 6; 2026: 3.

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  1. 2023A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validationcited by 91
  2. 2024Building Guardrails for Large Language Modelscited by 61
  3. 2021On Guaranteed Optimal Robust Explanations for NLP Modelscited by 54
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  6. 2024A review on data-driven constitutive laws for solidscited by 35
  7. 2021A Review of Formal Methods applied to Machine Learningcited by 33
  8. 2021Reachability Is NP-Complete Even for the Simplest Neural Networkscited by 27
  9. 2021DNNV: A Framework for Deep Neural Network Verificationcited by 23
  10. 2023Training robust and generalizable quantum modelscited by 21
  11. 2022PRoA: A Probabilistic Robustness Assessment against Functional Perturbationscited by 19
  12. 2022Verification-Aided Deep Ensemble Selectioncited by 18
38 more
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  5. 2023From Robustness to Explainability and Back Againcited by 14
  6. 2022Reachability Analysis of a General Class of Neural Ordinary Differential Equationscited by 13
  7. 2023Provable Preimage Under-Approximation for Neural Networks (Full Version)cited by 13
  8. 2021Towards Practical Robustness Analysis for DNNs based on PAC-Model Learningcited by 12
  9. 2021Infinite Time Horizon Safety of Bayesian Neural Networkscited by 12
  10. 2023POLAR-Express: Efficient and Precise Formal Reachability Analysis of Neural-Network Controlled Systemscited by 12
  11. 2021Sparse Adversarial Video Attacks with Spatial Transformationscited by 11
  12. 2021On the Impact of Hard Adversarial Instances on Overfitting in Adversarial Trainingcited by 11
  13. 2021Curriculum Learning for Safe Mapless Navigationcited by 11
  14. 2023Towards Verifying the Geometric Robustness of Large-scale Neural Networkscited by 11
  15. 2023Verifying Generalization in Deep Learningcited by 11
  16. 2024A Survey on Verification and Validation, Testing and Evaluations of Neurosymbolic Artificial Intelligencecited by 10
  17. 2024ProTIP: Probabilistic Robustness Verification on Text-to-Image Diffusion Models against Stochastic Perturbationcited by 10
  18. 2021Analyzing Human Models that Adapt Onlinecited by 8
  19. 2021ε-weakened Robustness of Deep Neural Networkscited by 8
  20. 2022Hierarchical Distribution-Aware Testing of Deep Learningcited by 8
  21. 2022Provably Tightest Linear Approximation for Robustness Verification of Sigmoid-like Neural Networkscited by 8
  22. 2023Reachability Analysis of Neural Network Control Systemscited by 8
  23. 2024PREMAP: A Unifying PREiMage APproximation Framework for Neural Networkscited by 8
  24. 2021A Scalable Two Stage Approach to Computing Optimal Decision Setscited by 7
  25. 2022Certified Policy Smoothing for Cooperative Multi-Agent Reinforcement Learningcited by 7
  26. 2021Customizable Reference Runtime Monitoring of Neural Networks using Resolution Boxescited by 6
  27. 2022Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systemscited by 6
  28. 2023What, Indeed, is an Achievable Provable Guarantee for Learning-Enabled Safety Critical Systemscited by 6
  29. 2023Reward Certification for Policy Smoothed Reinforcement Learningcited by 6
  30. 2024Unifying Qualitative and Quantitative Safety Verification of DNN-Controlled Systemscited by 6
  31. 2024Trustworthy Text-to-Image Diffusion Models: A Timely and Focused Surveycited by 6
  32. 2025Probabilistic Robustness in Deep Learning: A Concise yet Comprehensive Guidecited by 6
  33. 2026Embodied Foundation Models at the Edge: A Survey of Deployment Constraints and Mitigation Strategiescited by 6
  34. 2021Fooling Object Detectors: Adversarial Attacks by Half-Neighbor Maskscited by 5
  35. 2021Adversarial Robustness Guarantees for Gaussian Processescited by 5
  36. 2021Static analysis of ReLU neural networks with tropical polyhedracited by 5
  37. 2021Adversarial Robustness of Deep Learning: Theory, Algorithms, and Applicationscited by 5
  38. 2022Reachability In Simple Neural Networkscited by 5

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